[1] Chen Z, Bunger A P, Zhang X, et al. Cohesive zone finete element-based modling of hydraulic fractures[J]. Acta Mechanica Solida Sinica, 2009, 22(5): 443-452.
[2] Wang W, Dahi Taleghani A. Emergence and propagation of delamination cracks along the casing-cement interface[C]. ARMA 12-449, 46th US Rock Mechanics/Geomechanics Symposium. Chicago, IL, USA, June 24-27, 2012.
[3] Zhang G M, Liu H, Zhang J, et al. Three-dimensional finite element simulation and parametric study for horizontal well hydraulic fracture[J]. Journal of Petroleum Science and Engineering, 2010, 72(3): 310-317.
[4] Nagel N, Damjanac B, Garcia X, et al. Discrete element hydraulic fracturing modeling -evaluating changes in fracture transmissivity[C]. Canadian Unconventional Resources Conference. Alberta, Canada, November 15-17, 2011.
[5] Rahman M M, Hossain M M, Crosby D G, et al. Analytical, numerical and experimental investigations of transverse fracture propagation from horizontal wells[J]. Journal of Petroleum Science and Engineering, 2002, 35(3-4): 127-150.
[6] Hossain M M, Rahman M K. Numerical simulation of complex fracture growth during tight reservoir stimulation by hydraulic fracturing[J]. Journal of Petroleum Science and Engineering, 2008, 60(2): 86-104.
[7] Zhang X, Jeffrey R G, Bunger A P, et al. Initiation and growth of a hydraulic fracture from a borehole under toughness-or viscosity-dominated conditions[C]. ARMA 10-148, 44th US-Canada Rock Mechanics Symposium. Salt Lake City, UT, USA, June 27-30, 2010.
[8] Zhang X, Jeffrey R G, Thiercelin M. Mechanics of fluid-driven fracture growth in naturally fractured reservoirs with simple network geometries[J]. Journal of Geophysical Research, 2009, 114(B12): 402-406.
[9] Nagel N B, Sanchez-Nagel M, Lee B. Gas shale hydraulic fracturing: a numerical evaluation of the effect of geomechanical parameters[C]. SPE 152192, SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, USA, February 6-8, 2012.
[10] Tang C A, Tham L G, Lee P K K. Coupling analysis of flow,stress and damage (FSD) in rock failure[J]. International Journal of Rock Mechanics and Mining Sciences, 2002, 39(4): 477-489.
[11] Yang T H, Tham L G, Tang C A, et al. Influence of heterogeneity of mechanical properties on hydraulic fracturing in permeable rocks[J]. Rock Mechanics and Rock Engineering, 2004, 37(4): 251-275.
[12] Wang S Y, Sun L, Au A S K, et al. 2D-numerical analysis of hydraulic fracturing in heterogeneous geo-materials[J]. Construction and Building Materials, 2009, 23(6): 2196-2206.
[13] 薛炳, 张广明, 吴恒安, 等. 油井水力压裂的三维数值模拟[J]. 中国科 学技术大学学报, 2008, 38(11): 1322-1325. Xue Bing, Zhang Guangming, Wu Heng'ang, et al. Hydraulic fracturing three -dimensional numerical simulation in oil well[J]. Journal of China Science and Technology University, 2008, 38(11): 1322-1325.
[14] 连志龙, 张劲, 王秀喜, 等. 水力压裂扩展特性的数值模拟研究[J]. 岩 土力学, 2009,30(1): 169-174. Lian Zhilong, Zhang Jin, Wang Xiuxi, et al. Simulation study of characteristics of hydraulic fracturing propagation[J]. Rock and Soil mechanics, 2009, 30(1): 169-174.
[15] Yao Y, Gosavi S V, Searles K H, et al. Cohesive fracture mechanics based analysis to model ductile rock fracture[C]. ARMA 10-140, 44th US Rock Mechanics Symposium and 5th US-Canada Rock Mechanics Symposium. Salt Lake City, UT, USA, June 27-30, 2010.
[16] 张广明, 刘合, 张劲, 等. 油井水力压裂流-固耦合非线性有限元数值 模拟[J]. 石油学报, 2009, 30(1): 113-116. Zhang Guangming, Liu He, Zhang Jin. et al. Simulation of hydraulic fracturing of oil well based on fluid-solid coupling equation and non-linear finite element[J]. Acta Petrolei Sinica, 2009, 30(1): 113-116.
[17] 彪仿俊, 刘合, 张士诚, 等. 水力压裂水平裂缝影响参数的数值模拟 研究[J]. 工程力学, 2011(10): 228-235. Biao Fangjun, Liu He, Zhang Shicheng, et al. Numerical simulation on hydraulic fracturing horizontal fracture affecting parameters[J]. Engineering Mechanics, 2011(10): 228-235.
[18] 朱君, 叶鹏, 王素玲, 等. 低渗透储层水力压裂三维裂缝动态扩展数 值模拟[J]. 石油学报, 2010, 31(1): 119-123. Zhu Jun, Ye Peng, Wang Suling, et al. 3D numerical simulation of fracture dynamic propagation in hydraulic fracturing of low-permeability reservoir[J]. Acta Petrolei Sinica, 2010, 31(1): 119-123.
[19] 王素玲, 姜民政, 刘合. 基于损伤力学分析的水力压裂三维裂缝形态 研究[J]. 岩土力学, 2011(7): 2205-2210. Wang Suling, Jiang Mingzheng, Liu He. Study on hydraulic fracturing three-dimensional fracture morphology based on damage mechanics analysis[J]. Rock and Soil Mechanics, 2011(7): 2205-2210.
[20] 王瀚, 刘合, 张劲, 等. 水力裂缝的缝高控制参数影响数值模拟研究[J]. 中国科学技术大学学报, 2011(9): 820-825. Wang Han, Liu He, Zhang Jin, et al. Numerical simulation on affecting parameters of fracture height control in hydraulic fracture[J]. Journal of China Science and Technology University, 2011(9): 820-825.
[21] Barree R D, Conway M W. Experimental and Numerical Modeling of Convective Proppant Transport (includes associated papers 31036 and 31068)[J]. Journal of Petroleum Technology, 1995, 47(3): 216-222.
[22] 刘合, 张广明, 张劲, 等. 油井水力压裂摩阻计算和井口压力预测[J]. 岩石力学与工程学报, 2010, 29(增1): 2833-2839. Liu He, Zhang Guangming, Zhang Jin, et al. Friction loss calculation and surface pressure prediction in oil well hydrualic fracturing[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(S1): 2833-2839.
[23] Willingham J D, Tan H C, Norman L R. Perforation friction pressure of fracturing fluid slurries[C]. SPE 25891, Low Permeability Reservoirs Symposium, Denver, CO, USA, April 26-28, 1993.
[24] 郭建春, 杨立君, 赵金洲, 等. 压裂过程中孔眼摩阻计算的改进模型 及应用[J]. 天然气工业, 2005, 25(5): 69-71. GUO Jianchun, Yang Lijun, Zhao Jinzhou, et al. Modified model and application of calculation perforation pressure loss during hydraulic fracturing[J]. Natural Gas Industry, 2005, 25(5): 69-71.
[25] Romero J, Mack M G, Elbel J L. Theoretical model and numerical investigation of near -wellbore effects in hydraulic fracturing[J]. SPE Production & Facilities, 2000, 15(2): 76-82.
[26] Lord D L, Shah S N, Rein J R G, et al. Study of perforation friction pressure employing a large -scale fracturing flow simulator[C]. SPE 28508, SPE Annual Technical Conference and Exhibition, New Orleans, LA, USA, September 25-28 , 1994.
[27] 张广明, 刘合, 张劲, 等. 水平井水力压裂的三维有限元数值模拟研 究[J]. 工程力学, 2011(2): 101-106. Zhang Guangming, Liu He, Zhang Jin, et al. Three-dimensional finite element simulation and parametric study for horizontal well hydraulic fracture[J]. Engineering Mechanics, 2011(2): 101-106.